Manchester City defender Laporte, 27, was granted Spanish citizenship recently, having never played a senior game for France.
Alvaro Morata missed the best chance of the game late on when he hit the bar.
Portugal’s only shot on target was the last touch but Danilo Pereira’s header was straight at Unai Simon.
Spain had the better chances but Morata and Ferran Torres in particular were wasteful.
Cristiano Ronaldo had a quiet game for Portugal, glancing a header wide and failing to take a one-on-one opportunity.
Before kick-off, there was an announcement that the neighbours will make a joint bid to host the 2030 World Cup.
Both these sides have one more Euro 2020 warm-up left – Spain play Lithuania in Madrid on Tuesday before Portugal face Israel the next day in Lisbon.